[Paper Review] Postselection Strategies for Continuous-Variable Quantum Key Distribution Protocols with Quadrature Phase-Shift Keying Modulation

Florian Kanitschar, Christoph Pacher|arXiv (Cornell University)|Apr 19, 2021

Quantum Information and Cryptography23 references4 citations

TL;DR

This paper proposes a cross-shaped postselection strategy for continuous-variable quantum key distribution (CV-QKD) with quadrature phase-shift keying modulation, significantly improving secure key rates over long distances and high noise levels. Using numerical security proofs, it demonstrates that even with 80% of raw data discarded, the key rate remains over 80% of the non-postselected case, outperforming radial postselection in both trusted and untrusted detector models.

ABSTRACT

We use a recent numerical security proof technique to analyse three different postselection strategies for continuous-variable quantum key distribution protocols (CV-QKD) with quadrature phase-shift keying modulation. For all postselection strategies studied we provide novel analytical results for the operators that define the respective regions in phase space. In both, the untrusted and trusted detector model, a new, cross-shaped postselection strategy, clearly outperforms a state-of-the-art radial postselection scheme for higher transmission distances and higher values of noise. Motivated by the high computational effort for the error-correction phase we also studied the case when a large fraction of the raw key is eliminated by postselection: We observe that the secure key rate in case that only $20\%$ of the raw key passes the cross-shaped postselection is still roughly $80\%$ of the secure key rate without postselection for low values of excess noise and roughly $95\%$ for higher values of excess noise. Furthermore, we examine a strategy with radial and angular postselection that combines both the advantages of state-of-the-art radial postselection schemes and our cross-shaped strategy at the cost of higher complexity. Employing the cross-shaped postselection strategy, that can easily be introduced in the data processing, both new and existing CV-QKD systems can improve the achievable secure key rates significantly.

Motivation & Objective

• To analyze and improve postselection strategies in continuous-variable quantum key distribution (CV-QKD) with quadrature phase-shift keying (QPSK) modulation.
• To evaluate the performance of different postselection strategies under realistic conditions, including high excess noise and long transmission distances.
• To reduce the computational cost of error correction by minimizing the amount of raw key processed through effective postselection.
• To identify a practical, easily implementable postselection method that enhances secure key rates in existing and new CV-QKD systems.

Proposed method

• The authors employ a recent numerical security proof technique to analyze three postselection strategies in both trusted and untrusted detector models.
• They derive novel analytical expressions for the phase-space operators defining the cross-shaped and radial postselection regions.
• The cross-shaped strategy is designed to target specific regions in phase space that maximize information extraction while minimizing noise impact.
• A hybrid radial-angular postselection strategy is introduced to combine the advantages of both radial and cross-shaped methods at the cost of increased complexity.
• The performance is evaluated under varying levels of excess noise and transmission distances, focusing on secure key rate and computational load.
• The study quantifies the trade-off between postselection efficiency and key rate, particularly when only 20% of the raw key survives postselection.

Experimental results

Research questions

• RQ1 How does the cross-shaped postselection strategy compare to radial postselection in terms of secure key rate under high excess noise and long distances?
• RQ2 What is the impact of postselecting only 20% of the raw key on the final secure key rate in the presence of excess noise?
• RQ3 Can a hybrid radial-angular postselection strategy combine the benefits of both radial and cross-shaped methods while remaining practical?
• RQ4 How does the computational cost of error correction scale when using aggressive postselection strategies like the cross-shaped method?
• RQ5 To what extent can existing CV-QKD systems benefit from implementing the cross-shaped postselection strategy without hardware changes?

Key findings

• The cross-shaped postselection strategy outperforms radial postselection in both trusted and untrusted detector models, especially at high transmission distances and high excess noise levels.
• When only 20% of the raw key passes through the cross-shaped postselection, the secure key rate remains approximately 80% of the non-postselected key rate for low excess noise.
• For higher excess noise levels, the secure key rate after 20% postselection remains around 95% of the non-postselected rate, indicating strong resilience to noise.
• The hybrid radial-angular postselection strategy successfully combines the advantages of both radial and cross-shaped methods but incurs higher implementation complexity.
• The cross-shaped strategy can be easily integrated into existing and new CV-QKD systems, enabling significant improvements in achievable secure key rates without hardware modifications.